Abstract
We introduce a number of new tools for the study of relatively
hyperbolic groups. First, given a relatively hyperbolic
group G, we construct a nice combinatorial
Gromov hyperbolic model space acted on properly by G, which reflects
the relative hyperbolicity of G in many natural ways. Second, we
construct two useful bicombings on this space. The first of these,
preferred paths, is combinatorial in nature and allows us to
define the second, a relatively hyperbolic version of a construction
of Mineyev.
As an application, we prove a group-theoretic analog of the
Gromov-Thurston 2\pi Theorem in the context of relatively hyperbolic
groups.